New Perturbation Bounds for the Unitary Polar Factor
Ren-Cang Li
EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-94-852
December 1994
http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/CSD-94-852.pdf
Let A be an m x n (m >= n) complex matrix. It is known that there is a unique polar decomposition A = QH, where Q*Q = I, the n x n identity matrix, and H is positive definite, provided A has full column rank. This note addresses the following question: how much may Q change if A is perturbed? For the square case m = n our bound, which is valid for any unitarily invariant norm, is sharper and simpler than Mathias's (SIAM J. Matrix Anal. Appl., 14 (1993), 588-597.). For the non-square case, we also establish a bound for unitarily invariant norm, which has not been done in literature.
BibTeX citation:
@techreport{Li:CSD-94-852,
Author = {Li, Ren-Cang},
Title = {New Perturbation Bounds for the Unitary Polar Factor},
Institution = {EECS Department, University of California, Berkeley},
Year = {1994},
Month = {Dec},
URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5883.html},
Number = {UCB/CSD-94-852}
}
EndNote citation:
%0 Report %A Li, Ren-Cang %T New Perturbation Bounds for the Unitary Polar Factor %I EECS Department, University of California, Berkeley %D 1994 %@ UCB/CSD-94-852 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5883.html %F Li:CSD-94-852